Five fraction activities fit in a 40-minute session with paper, tape and a recipe card. Each one asks a different question: what the whole is, where a number sits, how an amount changes, when a rule holds, and what can be compared. They are starting points to adapt to your class, with sample answers to help you discuss the reasoning.
| Activity | Materials | Minutes | What the class should explain |
|---|---|---|---|
| Folded strips | Two paper strips | 8 | Why two different fractions can have the same value |
| Number line with cards | Tape and five cards | 8 | What distance from 0 each number shows |
| Scaled recipe | One card with amounts | 8 | Which factor changes each amount |
| Wrong sum | Two cards | 6 | Which step fails and how to check it |
| Bars | Paper drawings | 5 | What is being compared: numbers or lengths |
The times add up to 35 minutes; the other 5 are for fixing the meaning of the whole at the start, and the wrap-up happens inside each activity’s time. To organize your ideas before and after the session, the teaching fractions guide explains the sequence and the reason for each representation, and the teacher resources page collects printable material.
Fold strips to see equivalent fractions
Fold a paper strip in half and shade one part. Fold another strip of the same size into four equal parts and shade two. Line both up at the left end and ask: “What part of each strip is shaded? Are the shaded regions the same length?”
The first strip shows 1/2 and the second 2/4. Both represent the same whole, so the shaded regions have the same length: the fractions are equivalent. The numeric check is to multiply the numerator and denominator by 2. To try another pair, ask for 3/4 and 6/8 on strips of equal size.
One question separates two ideas: “Are four parts worth twice as much as two?” No, because each fourth is half of a half. And if one strip is 12 cm long and the other 16 cm, the fraction is the same but the shaded lengths would be 6 cm and 8 cm. Equivalence is about the number, not the physical length.
Place cards on a number line that can extend
Prepare masking tape, five cards with 1/4, 5/4, 3/2, 7/4 and −1/2, and visible marks for 0 and 1. Leave room on both sides, because the line does not end at the starting marks. The prompt is “Place each card and justify its distance from 0.”
If the stretch from 0 to 1 is divided into four equal parts, 1/4 sits at the first mark. One fourth past 1 is 5/4, which is 1 + 1/4; 3/2 is halfway between 1 and 2, and 7/4 is one fourth short of 2. To the left of 0, half a unit back gives −1/2. Before wrapping up, measure: the stretch from 0 to 1 and the one from 1 to 2 must be equal.
A possible mistake is to put 5/4 on the fifth mark of a scale with five parts between 0 and 1. Ask learners to name what each interval is worth; that fifth mark is worth 1. A fraction can be greater than 1 or negative, and the interactive fraction number line helps check positions after the discussion. The Common Core standard 3.NF.A.2 asks learners to place fractions on a number line in the same way, by splitting the interval from 0 to 1 into equal parts.
Scale a recipe from 4 to 6 servings
Write a made-up recipe on a card: 4 servings use 3/4 cup of water and 1/8 cup of oil. Now 6 servings are needed, with the same amount per serving. Before calculating, ask whether more or less water will be needed than for 4 servings.
Worked example: the water in the recipe
A recipe for 4 servings uses 3/4 cup of water. How much water is needed for 6 servings?
- Find the factor. 6 servings divided by 4 servings is 6/4, which simplifies to 3/2.
- Multiply the amount by the factor. 3/4 × 3/2 = 9/8.
- Write it as a mixed number if that helps. 9/8 = 1 1/8 cups.
- Apply the same factor to the oil. 1/8 × 3/2 = 3/16 cup.
Result: 1 1/8 cups of water and 3/16 cup of oil.
Check. Each serving takes (3/4) ÷ 4 = 3/16 cup of water. Six servings are 18/16, the same as 9/8.
As a follow-up, ask “What if we add 2 cups to each amount?” That addition does not keep the recipe’s proportions, because the oil would be multiplied by more than ten and the water by less than four. Scaling multiplies everything by the same factor. A cup does not measure the same everywhere (a US cup is about 237 ml), so converting to grams needs an equivalence specific to each ingredient. With the units in view, scale recipes lets you repeat the change with other numbers.
Investigate a wrong sum
Write “1/3 + 1/4 = 2/7” on one card and leave another blank for the correction. Present it as a calculation to review, without saying who did it. The prompt is “Find the step that fails and give a check that does not repeat the calculation.”
Ask the class to work out which rule produces 2/7 and to show, by comparing 2/7 with 1/3, that it cannot be right. Then it is worth testing the opposite rule, “never add numerators,” which is also false: 2/5 + 1/5 = 3/5. Numerators are added when the parts are the same size; if not, convert to comparable parts first. The fraction practice page offers more sums to explain.
Compare drawings and decide what is being compared
Draw two bars of the same size. Divide the first into three equal parts and shade two; divide the second into five and shade three. Ask which has the larger shaded part. The fractions are 2/3 and 3/5; in fifteenths, 2/3 = 10/15 and 3/5 = 9/15, so 2/3 is greater.
Then change the size of the bars. The order of 2/3 and 3/5 does not change, but the shaded length does. 2/3 of a 6 cm bar is 4 cm, and 3/5 of a 10 cm bar is 6 cm. The second shaded region is longer even though its fraction is smaller. Ask learners to point out the whole before comparing, and review the results with visual fractions.
A 40-minute session
Start with 5 minutes to fix the meaning of the whole, and write three questions on the board: what is the whole, how large is each part, and what does the answer check. Then follow the order in the table. In each activity, ask for a prediction, the calculation or drawing, and a check. This is a suggested schedule; spend more time on the step your group needs to explain, and see why fractions must refer to the same whole if that idea is hard.
To wrap up, within the time of each activity, pick one answer from each activity and ask learners to name the whole, what each part represents and how it is checked. If an answer changes when the context changes, they should say which condition changed.
Exit questions
- Write a fraction equivalent to 1/2 that has denominator 8.
- A strip is 12 cm long. How long is 5/6 of the strip?
- The strip is now 18 cm long. How long is 5/6 of the strip?
Show the answers
- 4/8, because 1/2 = 4/8 when you multiply top and bottom by 4.
- 10 cm: each sixth is 2 cm long and you take five of them.
- 15 cm: each sixth is 3 cm long. The fraction is the same, but the whole changed (12 cm versus 18 cm), so the part measured changed too.
If someone answers 5 cm to the second question by looking only at the numerator, or 2 cm by stopping at a single sixth, ask how long each sixth is and how many sixths are taken. If an answer has no unit, add the centimeters.
Change the support, not the question
If folding into equal parts is hard, hand out a strip that is already marked and ask learners to label the parts. Once the representation is clear, have them draw another equivalent pair, such as 4/10 and 2/5. On the number line, start with only 0, 1 and 2, and add negatives or numbers greater than 1 once the scale is steady.
In the recipe, keep the units in view and use a simple factor. In the comparison, change the size of the wholes only after solving with a shared whole, to separate two goals: ordering fractions and measuring quantities. For pair work, one person draws or folds and the other checks the whole, the equality of the parts and the written fraction; then they swap roles. If the activity needs many sheets, create fraction worksheets explains how to prepare them, and the fraction worksheets page has sets to practice with afterward.
Sources
The prompts on this page are original. The Common Core fractions standards for grade 3 (3.NF.A.1 to 3.NF.A.3) cover fractions as equal parts of a whole, placing fractions on a number line, and recognizing equivalent fractions such as 1/2 and 2/4, the ideas behind the first two activities.
- Common Core State Standards Initiative, “Grade 3, Number and Operations: Fractions,” accessed October 17, 2026. thecorestandards.org